Abstract
The Fock space relativistic coupled cluster method (FS-RCC) is one of the most promising tools of electronic structure modeling for atomic and molecular systems containing heavy nuclei. Until recently, capabilities of the FS-RCC method were severely restricted by the fact that only single and double excitations in the exponential parametrization of the wave operator were considered. We report the design and the first computer implementation of FS-RCC schemes with full and simplified non-perturbative account for triple excitations in the cluster operator. Numerical stability of the new computational scheme and thus its applicability to a wide variety of molecular electronic states is ensured using the dynamic shift technique combined with the extrapolation to zero-shift limit. Pilot applications to atomic (Tl, Pb) and molecular (TlH) systems reported in the paper indicate that the breakthrough in accuracy and predictive power of the electronic structure calculations for heavy-element compounds can be achieved. Moreover, the described approach can provide a firm basis for high-precision modeling of heavy molecular systems with several open shells, including actinide compounds.
Highlights
The ultimate goal of modern relativistic quantum chemistry is the development of highly accurate ab initio methods of electronic structure modeling for studying atomic and molecular electronic structure, being applicable to systems with general geometry and shell structure, with emphasis on species containing heavy or super-heavy elements
Special relativity is fundamental for understanding chemical behavior of heavy elements [2,3], and the non-relativistic Hamiltonian can no longer serve as a good model for description of electronic subsystem and has to be replaced by other models derived from the relativistic consideration of particle motion, e.g., those based on the Dirac-Coulomb or
Pilot applications of the presented Fock space (FS)-RCCSDT and FS-RCCSDT-n schemes to atomic (Tl, Pb) and molecular (TlH) systems clearly demonstrate the importance of accounting for triple excitations in relativistic coupled cluster models for achieving really high accuracy
Summary
The ultimate goal of modern relativistic quantum chemistry is the development of highly accurate ab initio methods of electronic structure modeling for studying atomic and molecular electronic structure, being applicable to systems with general geometry and shell structure, with emphasis on species containing heavy or super-heavy elements. The most natural way to treat a manifold of quasi-degenerate problems such as excited states and bond breaking one should use multi-reference (MR) approaches, providing the flexibility needed to describe wavefunctions in such challenging cases [5] For this reason, considerable efforts have been made to formulate MR methods and provide their implementations as general-purpose computer codes. In addition the development of high-precision electronic structure methods is directed towards (i) improving the approximation of the Hamiltonian by inclusion of high-order relativistic and QED effects; (ii) improving the dynamic correlation treatment by increasing the excitation rank of cluster operators (in case of coupled cluster methods) or the perturbation theory (PT) order; and/or (iii) improving the non-dynamic correlation treatment by increasing size of the active valence or model (P) space, (iv) converging basis set to completeness. Please note that energy calculations were conducted and reported (Sections 3.1 and 3.2), and potential benefits for high-precision calculations of properties are revealed on the example of static dipole polarizability (Section 3.3)
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